Компьютерное моделирование задач аэрогидродинамики на основе численного решения кинетического уравнения методом решеточных уравнений Больцмана в программном комплексе XFlow



Computer Simulation of Aerohydrodynamics Problems on the Base of Numerical Solution of Kinetic Equation by Lattice Boltzmann Method in the XFlow software package

There are demonstrated the possibilities of software package XFlow™ developed by Next Limit Technologies™ and designed to simulate a wide class flows of viscous heat-conducting liquids and gases. Numerical algorithm is based on the meshless method of Lagrangian particles to solving the Boltzmann equation for the distribution function with a certain type of collision integral. The basis of the numerical scheme is a solution of lattice Boltzmann equations, known in the literature as LBM - method (Lattice Boltzmann Method). For the simulation of turbulent flows the LES (Large Eddy Simulation) model of large-scale turbulence is used. XFlow™ has the ability to calculate the non-stationary two- and three-dimensional problems with complicated boundary conditions and moving bodies. There are presented the results of the simulation of external aerodynamics and internal hydrodynamics.

kinetic equation, lattice Boltzmann method, computational aero-and hydrodynamics, crystal growth, Czochralski hydrodynamic model

Наталья Владимирова, Анатолий Простомолотов, Наталия Верезуб

Том 16, выпуск 1, 2015 год



В работе демонстрируются возможности программного комплекса XFlow™, разрабатываемого компанией Next Limit Technologies™ для моделирования широкого класса течений вязких теплопроводных жидкостей и газов. Численный алгоритм основан на бессеточном методе Лагранжевых частиц решения кинетического уравнения Больцмана для функции распределения с определенным видом интеграла столкновений. В основу численной схемы положен LBM-метод (Lattice Boltzmann Method) решеточных уравнений Больцмана. Для моделирования турбулентных течений используется LES-модель турбулентности (Large Eddy Simulation). Алгоритм предназначен для моделирования нестационарных двумерных и пространственных задач со сложными граничными условиями и подвижными телами. Приведены результаты моделирования широкого класса задач внешней аэродинамики и внутренней гидродинамики.

кинетическое уравнение, метод решеточных уравнений Больцмана, вычислительная аэро- и гидродинамика, выращивание кристаллов, гидродинамическая модель метода Чохральского

Наталья Владимирова, Анатолий Простомолотов, Наталия Верезуб

Том 16, выпуск 1, 2015 год



1. XFlow 2014 User Guide. – © 2014 Next Limit Dynamics SL, 2014.
2. G. McNamara and G. Zanetti. Use of the Boltzmann equation to simulate lattice-gas automata // Physical Review Letters, pp. 61-2332, 1988.
3. F.J. Higuera and J. Jimenez. Boltzmann approach to lattice gas simulations // Europhysics Letters, pp. 9-663, 1989.
4. Y.H. Qian, D. D'Humieres, and P. Lallemand. Lattice BGK models for Navier-Stokes equation // Europhysics Letters, pp. 17-479, 1992.
5. S. Chen and G. Doolen. Lattice Bolzmann method for fluid flows // Annual Reviews of Fluid Me-chanics, pp. 30-329, 1998.
6. Zh. Guo, B. Shi,y and N. Wangy. Lattice BGK Model for Incompressible Navier–Stokes Equation // JCPh, v. 165 (2000), pp. 288.
7. S. Succi. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond // Clarendon Press, 2001.
8. Чепмен С., Каулинг Т. Д., Математическая теория неоднородных газов, пер. с англ., М., 1960.
9. Уленбек Дж., Форд Дж. Лекции по статистической механике, пер. с англ., М., 1965.
10. Maxwell J. B. Lattice Boltzmann methods for interfacial wave modeling // University of Edinburgh, 1997.
11. Sun C. Lattice-Boltzmann models for high speed flows // Phys. Rev. E. 1998. 58, N 6. 7283–7287.
12. Chen F., Xu A., Zhang G., Li Y. Three-dimensional lattice Boltzmann model for high-speed com-pressible flows // Commun. Theor. Phys. 2010. 54, N 6. 1121–1128.
13. He X., Luo L.-S. Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation // Phys. Rev. E. 1997. 56, N 6. 6811–6817.
14. Begum R., Basit M.A. Lattice Boltzmann method and its applications to fluid flow problems // European J. оf Scientific Research. 2008. 22, N 2. 216–231.
15. Bhatnagar P., Gross E.P., Krook M.K. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems // Phys. Rev. 1954. 94, N 3. 511–525.
16. Qian Y.H., d’Humi`eres D., Lallemand P. Lattice BGK models for Navier–Stokes equation // Euro-physics Letters.1992. 17, N 6. 479–484.
17. Aidun C.K., Clausen J.R. Lattice-Boltzmann method for complex flows // Annu. Rev. Fluid Mech. 2010. 42. 439–472.
18. Prostomolotov A.I., Verezub N.A., Vladimirova N.A. The surface flow structures in Czochralski hydrodynamic model // Proceedings of the International Conference "Fluxes and Structures in Fluids", June 25 – 28, 2013, St. Petersburg. - M.: MAKS Press, 2013. P. 254-256.
19. Prostomolotov A.I., Iliasov H.H., Verezub N.A., Vladimirova N.A. Application of XFlow™ code for numerical simulation of aero- and hydrodynamic structures // Selected Papers of the International Conference "Fluxes and Structures in Fluids - 2013". - M.: MAKS Press. 2014. P. 170-177.
20. Vladimirova N.A. CFD analysis and calculation of aerodynamic characteristics of helicopter rotor // Proceedings of the 39th European Rotorcraft Forum (ERF39), September 3-6, 2013, Moscow.
21. Vladimirova N.A., Verezub N.A., Prostomolotov A.I. Approbation of XFlowTM 2014 software code for modeling wave and vortex structures // Proceedings of the 5-th International Scientific School of Young Scientists "Waves and Vortices in Complex Media", November 25-28, Moscow. - M.: MAKS Press, 2014. P. 127-130.
22. Vladimirova N.A., Verezub N.A., Prostomolotov A.I. Numerical simulation of complicated wave and vortex structures by XFlowTM code // Proceedings of the 6-th International Scientific School of Young Scientists "Waves and Vortices in Complex Media", June 21-23, 2015, Kaliningrad. - M.: MAKS Press, 2015. P. 41-44.
23. Miller W., “Numerical simulation of bulk crystal growth on different scales: silicon and GeSi”, WILEY InterScience, Phys. Status Solidi B, vol.247, no.4, pp.885-869, 2010.
24. Mokhtari F., Bouabdallah A., Zizi M., Hanchi S., Alemany A., “Combined effects of crucible geo-metry and Marangony convection on silicon Czochralski crystal growth”, Cryst. Res. Technology, WILEY InterScience, vol.44, no.8, pp.787-799, 2009.
25. N.A. Verezub, E.V. Zharikov, A.Z. Myaldun, and A.I. Prostomolotov. The phenomenon of large-scale vortex formation induced on the surface of a liquid by vibration of solid body // A Journal of the Russian Academy of Sciences: PHYSICS-DOCLADY, vol. 41, No. 10, 1996, pp. 471-474.
26. D.C. Miller, T.L. Pernell. Fluid flow patterns in a simulated garnet melt // Journal of Crystal Growth, vol. 58 (1982), pp. 253-260.
27. C.J. Jing, M. Kobayashi, T. Tsukada, M. Hozawa, T. Fukuda, N. Imaishi, K. Shimamura, N. Ichi-nose. Effect of RF coil position on spoke pattern on oxide melt surface in Czochralski crystal growth // Journal of Crystal Growth, vol. 252 (2003), pp. 550–559.